Second order sufficient conditions and sensitivity analysis for optimal multiprocess control problems

Abstract

Second order sufficient optimality conditions (SSC) are derived for optima! multiprocess eontroi problems. For that pur­ pose the multiprocess control problem is transformed into a single stage control problem with augmented state variables which com­ prise the state variables of all individua.l sta.ges as well as the switch­ ing times as choice variables. This tra.nsforma.tion allows to a.pply the known SSC for single sta.ge control problems. A numerical t est of SSC involves the solution of an associa.ted R.iccati equation together with boundary conditions adapted to the multiprocess . Sensitivity analysis of pa.ra.metric multiprocess problems can be based on SSC. A numerical example of the optima! two- stage control of a robot illustrates both SSC and sensitivity analysis.